Are the following statements true or false? False 1. Finding an eigenvector of might be difficult, but checking whether a given vector is in fact an eigenvector is easy. False 2. A matrix is singular if and only if 0 is an eigenvalue of . False 3. If for some vector , then is an eigenvalue of . True 4. To find the eigenvalues of , reduce to echelon form. True 5. A number is an eigenvalue of if and only if the equation has a nontrivial solution .